As can be seen in the picture, almost all countries in North and South America (excluding island countries) unconditionally offer citizenship to anyone born in their territory. At the same time, almost all countries elsewhere don't do so. So, what makes North and South America special?
The countries in the Americas were founded by colonial settlers declaring independence from their corresponding colonial power, predominately at the end of the 18th and the beginning of the 19th century. To distinguish an American from a British person in 1777, ancestry is not that helpful. Place of birth, much more so. In the former Spanish colonies, this is compounded by a social system that gave preference to recent immigrants over locally-born descendants of Spaniards.
Other settler-colonies, South Africa, New Zealand and Australia, still have mixed-forms. What sets them apart from most nations in the Americas is timing and method of gaining independence.
Cynical answer? It's to justify the suppression of native peoples by immigrant cultures and their largely European ruling classes. If they establish a right to residence based on ancestry, then they're giving native people rights senior to their own. And what self-respecting colonialist would ever do such a thing? Instead, you establish rights that favour your own interests at the expense of others'. And now that the native peoples are outnumbered by the immigrants and their descendants, you can further suppress native interests based on majority rule.